Evaluate 2sin(45 degrees )+4cos(30 degrees )

Problem

2*sin(45)+4*cos(30)

Solution

1. Identify the exact values for the trigonometric functions at the given angles.

2. Substitute the value sin(45)=√(,2)/2 into the expression.

3. Substitute the value cos(30)=√(,3)/2 into the expression.

4. Multiply the coefficients by the substituted values.

2*(√(,2)/2)+4*(√(,3)/2)

5. Simplify the terms by canceling the common factors in the numerators and denominators.

√(,2)+2√(,3)

Final Answer

2*sin(45)+4*cos(30)=√(,2)+2√(,3)

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